Variable screening and graphical modeling for ultra-high dimensional longitudinal data

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dc.contributor.authorZhang, Yafeien
dc.contributor.committeechairDu, Pangen
dc.contributor.committeememberWu, Xiaoweien
dc.contributor.committeememberKim, Inyoungen
dc.contributor.committeememberHong, Yilien
dc.contributor.departmentStatisticsen
dc.date.accessioned2020-12-24T07:00:36Zen
dc.date.available2020-12-24T07:00:36Zen
dc.date.issued2019-07-02en
dc.description.abstractUltrahigh-dimensional variable selection is of great importance in the statistical research. And independence screening is a powerful tool to select important variable when there are massive variables. Some commonly used independence screening procedures are based on single replicate data and are not applicable to longitudinal data. This motivates us to propose a new Sure Independence Screening (SIS) procedure to bring the dimension from ultra-high down to a relatively large scale which is similar to or smaller than the sample size. In chapter 2, we provide two types of SIS, and their iterative extensions (iterative SIS) to enhance the finite sample performance. An upper bound on the number of variables to be included is derived and assumptions are given under which sure screening is applicable. The proposed procedures are assessed by simulations and an application of them to a study on systemic lupus erythematosus illustrates the practical use of these procedures. After the variables screening process, we then explore the relationship among the variables. Graphical models are commonly used to explore the association network for a set of variables, which could be genes or other objects under study. However, graphical modes currently used are only designed for single replicate data, rather than longitudinal data. In chapter 3, we propose a penalized likelihood approach to identify the edges in a conditional independence graph for longitudinal data. We used pairwise coordinate descent combined with second order cone programming to optimize the penalized likelihood and estimate the parameters. Furthermore, we extended the nodewise regression method the for longitudinal data case. Simulation and real data analysis exhibit the competitive performance of the penalized likelihood method.en
dc.description.abstractgeneralLongitudinal data have received a considerable amount of attention in the fields of health science studies. The information from this type of data could be helpful with disease detection and control. Besides, a graph of factors related to the disease can also be built up to represent their relationships between each other. In this dissertation, we develop a framework to find out important factor(s) from thousands of factors in longitudinal data that is/are related to the disease. In addition, we develop a graphical method that can show the relationship among the important factors identified from the previous screening. In practice, combining these two methods together can identify important factors for a disease as well as the relationship among the factors, and thus provide us a deeper understanding about the disease.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:20483en
dc.identifier.urihttp://hdl.handle.net/10919/101662en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectgraphical modelen
dc.subjectvariable screeningen
dc.subjectlongitudinal data analysisen
dc.titleVariable screening and graphical modeling for ultra-high dimensional longitudinal dataen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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